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Old 11th Oct 2004, 17:15   #1 (permalink)
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Compressibility effects

Could somebody please explain the theory behind compressibilty effects at high altitude / high speeds?
MAYDAYMAYDAY is offline  
Old 12th Oct 2004, 13:16   #2 (permalink)
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Hello Mayday. I've found compressibility blamed for all sorts of problems/analomies. The following is how I've come to appreciate it's effects.

Compressibility has 3 main influences that I see on aircraft and systems. Incompressible flow, ie without compressibility, occurs when density of the air can be considered a constant as it interacts with the aircraft. Generally less than .3 mach meets this criteria. Greater than .3 mach, and the variation can become important, particularly for aircraft with the performance envelope of today’s high subsonic airliners.

1. Airspeed measurement. Effects of compressibility on airspeed measurement can be seen form 7p3i7lot’s post above. Typically they are small, the effect on the cas is only typically up to 30 kts.

2. Lift. Effect of compressibility on the wing are much more difficult to understand and predict, and most texts do a poor job of explaining it. Experimental data shows that for .6 mach and less, for a given aoa, the value of Cl **can** actually be greater than without compressibility. That is, as you speed up, the Cl value for a fixed aoa can increase. The slope of the lift curve, delta CL divided by delta aoa, is greater with slight compressibility than no compressibility. Further, the max Cl value can be greater at a fixed mach, although as mach increases, a slight rise in max Cl seems to be followed by a drop to below the non compressible value of Cl max. And while von Mises “theory of flight” shows stall aoa to be greater with slight compressibility, I’ve not seen that in other texts. In fact, others show the stall aoa to be less with compressibility. Note that all of this is for an airfoil with flow entirely subsonic.

3. Drag. Although one may argue that it is not compressibiltity that affects drag in the transonic range, I generally consider it to be included. The coefficient of drag Cd is constant at low machs for a constant Cl. However as mach increases, there is a sudden and rapid increase in Cd as the effects of shock wave formation along the wing surfaces and flow separation come into play. Once complete supersonic flow envelopes the wing, a regular pattern of shock waves are formed, and an overall reduction of Cd occurs.

As KW typically says, “I could be all wrong”. I have no degree in an aerodyamic field, so this is all information I’ve gathered on the side.
Perhaps others have more pertinent, or correct information to add.

Make sense?

hawk37 is offline  
Old 12th Oct 2004, 13:41   #3 (permalink)
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A gas can be compressed, this means that when we exert an increasing pressure on a cilinder filled with gas, the volume of that unit of air will decrease. Liquids, like water, are as good as incompressible. Take a cilinder filled with water, put pressure on the top, and the water volume will hardly change with increasing pressure.

What is the result of this compressibility? Density changes. With increasing pressure a gas will have a density increase as well. With increasing pressure a liquid will not have a density increase, with a liquid, density will not change.

Now look at the formula's used in basic aerodynamics (Bernouilli, total pressure = static + dynamic pressure). As you should know, dynamic pressure depends on density. And since air is a gas, hence compressible, density will change. It will increase with increasing pressure.

But we never make this correction, most of the time we use a density value for air in "not moving" conditions. On the ground ie, it's 1.225kg/m**3. But when air is moving and being brought to a sudden stop, the density of the air will slightly increase because it will be compressed. So we make an error. We use a value for density to calculate dynamic pressure, but this value depends on the value of dynamic pressure itself. So I hope you understand something is wrong here. Dynamic pressure depends on density and density depends on dynamic pressure... so we can't really use the formula's anymore.

The higher the speed of the air, the more the real density (the density of "air under pressure" or "moving air being brought to a stop") will be higher than the density we use, the larger the error.

Now there have been clever engineers who calculated the errors because of compressibility: at what speeds are the errors in density between "not moving air" and "air under pressure being stopped" large enough to create a noticeable error? That's when we start to use compressibility correction factors. These factors allow us to use the "static" density of air, and depend on the speed of the air of course.

Hope this helps?

PS: Formula of Bernouilli can only be used for incompressible fluids, that's a basic requirement. However, at low speeds and low altitudes, the errors created are so small we can neglect them. It's far more easier to use Bernouilli than the alternatives available (thank god...). But at high speeds/high altitude we have to make corrections... but still easier than the alternatives.

Last edited by BraceBrace; 12th Oct 2004 at 13:52.
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